Hyperbolicity for log canonical pairs and the cone theorem
Hyperbolicity for log canonical pairs and the cone theorem
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DOI：
10.1007/s00029-019-0512-9
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发表时间：
2014-10
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通讯作者：
R. Svaldi
中科院分区：
文献类型：
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作者：
R. Svaldi
给定一个对数正则对，我们证明了它是成立的，假设在由的非klt轨迹引起的分层的开层中没有从仿射线与值的非常数映射。这意味着锥定理的推广，其中每条负极值射线都是由一条有理曲线张成的，该有理曲线是包含在其中一个开放层中的仿射线的副本的闭包。此外，我们给出了一个Nakai型判据来判定在上述条件下何时是充分的，并证明了在任意奇点情况下的部分结果。
Given a log canonical pair, we show thatis nef assuming there is no non-constant map from the affine line with values in the open strata of the stratification induced by the non-klt locus of. This implies a generalization of the Cone Theorem where each-negative extremal ray is spanned by a rational curve that is the closure of a copy of the affine line contained in one of the open strata of. Moreover, we give a criterion of Nakai type to determine when under the above conditionis ample and we prove some partial results in the case of arbitrary singularities.